{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TDLII4YTA33VUI7QKO2CDLQCXR","short_pith_number":"pith:TDLII4YT","canonical_record":{"source":{"id":"1606.02457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-08T08:56:30Z","cross_cats_sorted":[],"title_canon_sha256":"1c26101c921455ebd4fa2c07d1462643127454eaadd75c07bd8a61ef77694147","abstract_canon_sha256":"13c2cbdee6bbc8971641296ec5842e6b313502c063da7f8487c793ff9c24d4cd"},"schema_version":"1.0"},"canonical_sha256":"98d684731306f75a23f053b421ae02bc7276dd00c8ffb2b283a1ece7b6b76d18","source":{"kind":"arxiv","id":"1606.02457","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02457","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02457v1","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02457","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"TDLII4YTA33V","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDLII4YTA33VUI7Q","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDLII4YT","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TDLII4YTA33VUI7QKO2CDLQCXR","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-08T08:56:30Z","cross_cats_sorted":[],"title_canon_sha256":"1c26101c921455ebd4fa2c07d1462643127454eaadd75c07bd8a61ef77694147","abstract_canon_sha256":"13c2cbdee6bbc8971641296ec5842e6b313502c063da7f8487c793ff9c24d4cd"},"schema_version":"1.0"},"canonical_sha256":"98d684731306f75a23f053b421ae02bc7276dd00c8ffb2b283a1ece7b6b76d18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:41.330695Z","signature_b64":"87r1QkzsH2XP7dn6HfagRs7cR3FUWSWPAlM79x7y7k59MYcOjaM7BmSljJF98nelD/H1az0iaxoLdKG3Vm3uCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98d684731306f75a23f053b421ae02bc7276dd00c8ffb2b283a1ece7b6b76d18","last_reissued_at":"2026-05-18T01:12:41.330348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:41.330348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02457","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2i6Dv3OSRJufmsUzbm+fk6mJBmuS81cJ1Gfl3PsH8chK+srpnTqPzxIc7zQRWW1fYn3r78Thvq9QnFX8RkpoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:52:39.870412Z"},"content_sha256":"3a409f7bd046b8c1fe82f924dd025ca284a24fe9e17a826ff48d026f5a5d8010","schema_version":"1.0","event_id":"sha256:3a409f7bd046b8c1fe82f924dd025ca284a24fe9e17a826ff48d026f5a5d8010"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TDLII4YTA33VUI7QKO2CDLQCXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Spectra of Local Minima in Spin-Glass Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Boris Kryzhanovsky, Magomed Malsagov","submitted_at":"2016-06-08T08:56:30Z","abstract_excerpt":"The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the spectrum width, the depth of the global minimum. The experimental data are used to build the relations between these quantities and the model dimensionality N and find their asymptotic values for N goes to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02457","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHLgZocK2GJUcrdM/p4Iqo6gUW9cgymWpJRtLTogSSZkCbXdYjpSJPVrv96Jk1lgBc3OQ69p7pFwHWFw7HnQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:52:39.870749Z"},"content_sha256":"78c61cca5f7984158ad72b6a625ab4d04dd3790e4ee707601187e0060f421e80","schema_version":"1.0","event_id":"sha256:78c61cca5f7984158ad72b6a625ab4d04dd3790e4ee707601187e0060f421e80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDLII4YTA33VUI7QKO2CDLQCXR/bundle.json","state_url":"https://pith.science/pith/TDLII4YTA33VUI7QKO2CDLQCXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDLII4YTA33VUI7QKO2CDLQCXR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-04T15:52:39Z","links":{"resolver":"https://pith.science/pith/TDLII4YTA33VUI7QKO2CDLQCXR","bundle":"https://pith.science/pith/TDLII4YTA33VUI7QKO2CDLQCXR/bundle.json","state":"https://pith.science/pith/TDLII4YTA33VUI7QKO2CDLQCXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDLII4YTA33VUI7QKO2CDLQCXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TDLII4YTA33VUI7QKO2CDLQCXR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"13c2cbdee6bbc8971641296ec5842e6b313502c063da7f8487c793ff9c24d4cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-08T08:56:30Z","title_canon_sha256":"1c26101c921455ebd4fa2c07d1462643127454eaadd75c07bd8a61ef77694147"},"schema_version":"1.0","source":{"id":"1606.02457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02457","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02457v1","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02457","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"TDLII4YTA33V","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TDLII4YTA33VUI7Q","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TDLII4YT","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:78c61cca5f7984158ad72b6a625ab4d04dd3790e4ee707601187e0060f421e80","target":"graph","created_at":"2026-05-18T01:12:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the spectrum width, the depth of the global minimum. The experimental data are used to build the relations between these quantities and the model dimensionality N and find their asymptotic values for N goes to infinity.","authors_text":"Boris Kryzhanovsky, Magomed Malsagov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-08T08:56:30Z","title":"The Spectra of Local Minima in Spin-Glass Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02457","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3a409f7bd046b8c1fe82f924dd025ca284a24fe9e17a826ff48d026f5a5d8010","target":"record","created_at":"2026-05-18T01:12:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"13c2cbdee6bbc8971641296ec5842e6b313502c063da7f8487c793ff9c24d4cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-06-08T08:56:30Z","title_canon_sha256":"1c26101c921455ebd4fa2c07d1462643127454eaadd75c07bd8a61ef77694147"},"schema_version":"1.0","source":{"id":"1606.02457","kind":"arxiv","version":1}},"canonical_sha256":"98d684731306f75a23f053b421ae02bc7276dd00c8ffb2b283a1ece7b6b76d18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98d684731306f75a23f053b421ae02bc7276dd00c8ffb2b283a1ece7b6b76d18","first_computed_at":"2026-05-18T01:12:41.330348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:41.330348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87r1QkzsH2XP7dn6HfagRs7cR3FUWSWPAlM79x7y7k59MYcOjaM7BmSljJF98nelD/H1az0iaxoLdKG3Vm3uCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:41.330695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a409f7bd046b8c1fe82f924dd025ca284a24fe9e17a826ff48d026f5a5d8010","sha256:78c61cca5f7984158ad72b6a625ab4d04dd3790e4ee707601187e0060f421e80"],"state_sha256":"d168a0e782d5dc86989789bf8539ab71642a8fae4b677a640fb3973e8191e937"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lkab8Nqz2ZZvYa4DCLEZPIn5rORIuEAXP19Ax3s3fJ2bDRxOGpwsY0LVEMyaIUjteQKg/c7uY4hjOi8B+fShAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T15:52:39.872688Z","bundle_sha256":"c279471618648c6c2db329ffed1d6a1b48764c29c01da19f4e257cb9d50ef9c1"}}